FIR EQ questions (simple ones)

As promissed ... newbie questions...  be gentle :-)

Reading up on making FIRs by using the IFFT approach.  E.g. setup your
frequency shape then do the inverse FFT, multiply by a suitable window
and voila.

In the examples they set the power to 1 (does that mean real = 1, imag
= 0?) and all others to zero for the band they wanted.  Could you set
it to higher than one to amplify the band?

As another question, iirc the "magnitude" of a spectral component is
the length of the hypotnuese formed by the real/imag forming sides of a
right angle?  Are imag=0 lengths valid for the computation?  [say when
you have PCM audio].?

Tom

Tom St Denis wrote:
> As promissed ... newbie questions...  be gentle :-)

Welcome :-).


> Reading up on making FIRs by using the IFFT approach.  E.g. setup your
> frequency shape then do the inverse FFT, multiply by a suitable window
> and voila.

You don't need a winodw for frequency domain filtering. Just FFT /
multiply / IFFT.


> In the examples they set the power to 1 (does that mean real = 1, imag
> = 0?)

1.0 = 1.0 + 0.0 i

> and all others to zero for the band they wanted.  Could you set
> it to higher than one to amplify the band?

You can set it to whatever you like, as long as the length of the
non-zero part of the IFFT of the filter kernel is matched with your
frame overlapping length in the time domain. You must have N >= L + M,
where N is the FFT length, L the filter impulse response length, and M
the overlap length.

>
> As another question, iirc the "magnitude" of a spectral component is
> the length of the hypotnuese formed by the real/imag forming sides of a
> right angle?  Are imag=0 lengths valid for the computation?

In that case magnitude = abs(real).

> [say when
> you have PCM audio].?

The DFT of an audio vector generally has non-zero imaginary part. Real
vectors have a Hermitian-symmetric DFT (real part is symmetric,
imaginary part is antisymmetric). For example, the vector [1; 2 + i;
-1; 2 - i;] has a purely real IDFT (notice the zero imaginary parts at
the start and in the middle due to the antisymmetry constraint).

Regards,
Andor

Tom St Denis wrote:
> As promissed ... newbie questions...  be gentle :-)

Good to see you here!  :-)

> In the examples they set the power to 1 (does that mean real = 1, imag
> = 0?) and all others to zero for the band they wanted.  Could you set
> it to higher than one to amplify the band?

Yes and yes  (i.e., yes, it means real part = 1, imag. part = 0, and
yes, you can set it to higher than 1 to amplify -- food for thought:
you could also set it to something that is not a real number to
manipulate the phase of the components in that band)

> As another question, iirc the "magnitude" of a spectral component is
> the length of the hypotnuese formed by the real/imag forming sides of a
> right angle?  Are imag=0 lengths valid for the computation?  [say when
> you have PCM audio].?

The geometric "triangle" analogy is good, but you could also see it
as vectors in an Euclidean two-dimensional space -- the real part is
the x-coordinate and the imaginary part is the y-coordinate.

The magnitude of a complex number is imply given by:  (example of a
function in C for illustration purposes)

double magnitude (struct complex z)
{
     return sqrt (z.real*z.real + z.imag*z.imag);
}

(actually, in C99 there are built-in complex numbers -- which I'm
not familiar with, so the above code might be inadequate;  still,
it should work for illustration purposes)

Carlos
--

Andor wrote:
> Tom St Denis wrote:
> > As promissed ... newbie questions...  be gentle :-)
>
> Welcome :-).

Thanks.

> > Reading up on making FIRs by using the IFFT approach.  E.g. setup your
> > frequency shape then do the inverse FFT, multiply by a suitable window
> > and voila.
>
> You don't need a winodw for frequency domain filtering. Just FFT /
> multiply / IFFT.

Hmm.. I thought there was a wobble in the passband where the level of
the filter would not be flat unless you used a lot of FIR taps.

Sorry I'm not 100% engaged in the learning process [I've got three jobs
and various other passtimes occupying my brain time...].

>From what I read you had to get the rough FIR taps from the IFFT then
convolve it with a suitable window function (what makes one "suitable"
is something I'm gonna read more about) then you get the taps that
won't have such a horrible wobble but possibly a slower transistion
[from what I glanced].

> > In the examples they set the power to 1 (does that mean real = 1, imag
> > = 0?)
>
> 1.0 = 1.0 + 0.0 i

Well, when you put it that way :-)

> > and all others to zero for the band they wanted.  Could you set
> > it to higher than one to amplify the band?
>
> You can set it to whatever you like, as long as the length of the
> non-zero part of the IFFT of the filter kernel is matched with your
> frame overlapping length in the time domain. You must have N >= L + M,
> where N is the FFT length, L the filter impulse response length, and M
> the overlap length.

mmm, I don't see impulse response length in the creation phase of the
FIR [admitedly the book covers two methods of making FIRs and I've only
read the FFT approach in depth].

Thanks for the info.  I of course will continue reading in depth :-)
I've got some flights next week giving me a good 6 hours each way of
reading time.

Tom

Carlos Moreno wrote:
> Tom St Denis wrote:
> > As promissed ... newbie questions...  be gentle :-)
>
> Good to see you here!  :-)

Thanks.

> > In the examples they set the power to 1 (does that mean real = 1, imag
> > = 0?) and all others to zero for the band they wanted.  Could you set
> > it to higher than one to amplify the band?
>
> Yes and yes  (i.e., yes, it means real part = 1, imag. part = 0, and
> yes, you can set it to higher than 1 to amplify -- food for thought:
> you could also set it to something that is not a real number to
> manipulate the phase of the components in that band)

I'm not into messing with phase yet (though I have done the usual cute
tricks of negating a bandpass on one channel and such for stereo field
effects).

So a quick question.  you have the relationship mag = sqrt(imag^2 +
real^2) so what is the effect of sliding more value from real to imag
while keeping mag equal?  Does that just slide the band in the
time-domain?

Could the "negate the trebble of the left channel" trick be done by
setting up a FIR via the FFT method but instead of putting 1's in the
real part of the higher frequency bands you put the 1 in the imag part,
do the IFFT and use the values as taps?  [excuse if this is a stupid
question, I'm just asking an exploration question here :-)]

I noticed the EQ in my "new" [dang I'm 17,500$ in debt now...] car has
a tone mode where you set the bass, mid, trebble and it sets up what
looks like a 5 or 7 band EQ [I didn't count the bars].  It can go below
and above a center line which I assume is "1" because a flat EQ isn't
zero bandwidth.   I'm guessing it does a similar trick as the IFFT =>
FIR one.

> > As another question, iirc the "magnitude" of a spectral component is
> > the length of the hypotnuese formed by the real/imag forming sides of a
> > right angle?  Are imag=0 lengths valid for the computation?  [say when
> > you have PCM audio].?
>
> The geometric "triangle" analogy is good, but you could also see it
> as vectors in an Euclidean two-dimensional space -- the real part is
> the x-coordinate and the imaginary part is the y-coordinate.

Yeah, the diagrams they have all have cartesian plane with the lines
starting from 0,0 going to the imag/real points.  

Tom

Tom St Denis wrote:
...
> Hmm.. I thought there was a wobble in the passband where the level of
> the filter would not be flat unless you used a lot of FIR taps.

...
> >
> > You can set it to whatever you like, as long as the length of the
> > non-zero part of the IFFT of the filter kernel is matched with your
> > frame overlapping length in the time domain. You must have N >= L + M,
> > where N is the FFT length, L the filter impulse response length, and M
> > the overlap length.
>
> mmm, I don't see impulse response length in the creation phase of the
> FIR [admitedly the book covers two methods of making FIRs and I've only
> read the FFT approach in depth].

Ok, I see where I misunderstood you. The windowing operation is used to
design the FIR filter. That's fine. I thought you wanted to window the
data - this is done in spectral analysis to reduce leakage. It is not
required to window the data for frequency domain filtering.

> Thanks for the info.  I of course will continue reading in depth :-)
> I've got some flights next week giving me a good 6 hours each way of
> reading time.

Sounds like fun! 

:-)

Tom St Denis wrote:

>>yes, you can set it to higher than 1 to amplify -- food for thought:
>>you could also set it to something that is not a real number to
>>manipulate the phase of the components in that band)
> 
> I'm not into messing with phase yet (though I have done the usual cute
> tricks of negating a bandpass on one channel and such for stereo field
> effects).
> 
> So a quick question.  you have the relationship mag = sqrt(imag^2 +
> real^2) so what is the effect of sliding more value from real to imag
> while keeping mag equal?  Does that just slide the band in the
> time-domain?

More or less...  I mean, yes -- just careful with what you understand
as "slide the band";  you change the phase, meaning that the "sliding"
or the "delay" in the time-domain is different for each frequency in
the band.  It is easy to come up with simplified examples/situations
to illustrate the issue, but it may be quite tough to visualize the
effect in a real/normal time-domain signal.

> Could the "negate the trebble of the left channel" trick be done by
> setting up a FIR via the FFT method but instead of putting 1's in the
> real part of the higher frequency bands you put the 1 in the imag part,

Careful -- think about it  (I won't tell you the exact answer so that
you can analyze it and figure it out);  the effect of multiplying by
a complex number is:  the magnitude is multiplied by the magnitude of
the complex number, and the phase of the result is the sum of the two
phases (that is, you're *adding phase* by an amount given by the phase
of the number you're multipying by).

The hint:  what is the phase of a complex number with real part 0 and
positive imaginary part?  What about negative imaginary part?  What
about 0 imaginary and negative real part?

> I noticed the EQ in my "new" [dang I'm 17,500$ in debt now...] car 

*pheewww* ....  *The CAR* ...  For a split second there I thought you
had spent 17k on an equalizer!!!  I was already considering charging
you some 80 or 100 dollars per hour for online consulting services!!!
;-)

> looks like a 5 or 7 band EQ [I didn't count the bars].  It can go below
> and above a center line which I assume is "1" because a flat EQ isn't
> zero bandwidth.   I'm guessing it does a similar trick as the IFFT =>
> FIR one.

I'm not sure what you mean by the above -- it does sound like what you
have is a *Parametric* Equalizer, but either way, you could visualize
the process of filtering via FFT as an equivalent trick to the way we
would play with an equalizer's controls;  not sure if that was what
you meant to ask, though.

Carlos
--